BIZOMAT MAKEOS · Strength
Centrifuge Bowl Check (Self Hoop Stress, Liquid Ring Pressure, Total Hoop Stress, Speed Limit)
For a spinning centrifuge bowl or basket holding a ring of liquid, how high is the hoop stress from its own spin and from the liquid pressure, and how fast may it run?
Check of a thin cylindrical centrifuge bowl: the acceleration at the wall as a multiple of gravity (as the centrifugal force tool), the hoop stress from the spinning shell itself (density × rim speed squared), the pressure the spinning liquid ring puts on the wall, the hoop stress from that pressure (as the thick cylinder tool’s thin-wall value), the total hoop stress, and the highest speed for your allowable stress, since every stress grows with the square of the speed.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Bowl inside radius | mm | Inside radius of the bowl wall. |
| Wall thickness | mm | Wall thickness of the bowl. |
| Speed | rpm | Running speed. |
| Bowl material density | kg/m³ | Density of the bowl material. |
| Liquid density | kg/m³ | Density of the liquid or slurry. |
| Radius of the liquid surface | mm | Radius of the free liquid surface (the liquid fills the ring from here to the wall; equal to the wall radius when empty). |
| Allowable hoop stress | MPa | Allowable hoop stress for the bowl material, joints and duty. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Bowl inside radius
- What it is
- The radius from the axis to the inside surface of the bowl wall.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Radius, not diameter: halve the inside diameter.
What this means: Wall thickness
- What it is
- The thickness of the cylindrical bowl wall.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A thicker wall lowers the liquid ring stress; the self hoop stress rises slightly as the mean radius grows.
- Get it right
- Use the thinnest wall, allowing for corrosion and wear.
What this means: Speed
- What it is
- The rotational speed of the bowl in operation.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2000 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Hoop stresses rise with the square of speed.
- Get it right
- Use the highest speed the drive can reach, including overspeed.
What this means: Bowl material density
- What it is
- The density of the bowl wall material, which loads the wall with its own spinning mass.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 25000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7850 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The self hoop stress rises in direct proportion.
- Get it right
- Take it from the material data sheet.
What this means: Liquid density
- What it is
- The density of the liquid or slurry spinning in the bowl, which presses outward on the wall.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0 kg/m³ to 25000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The liquid pressure on the wall rises in direct proportion.
- Get it right
- Use the densest slurry or cake the bowl may carry.
What this means: Radius of the liquid surface
- What it is
- The radius from the axis to the free inner surface of the spinning liquid ring. The liquid fills from here out to the wall.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A smaller surface radius raises the liquid pressure on the wall.
- Get it right
- A smaller radius means a thicker liquid layer; use the smallest radius the overflow allows. Equal to the bowl radius means empty.
What this means: Allowable hoop stress
- What it is
- The hoop stress you allow in the bowl, taking into account the material, joints, welds and duty.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 5000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Set it from the centrifuge maker or the design code; welds and holes reduce it.
Method and formulas
- ω = 2π n ÷ 60; g-level = ω² r ÷ g (as the centrifugal force tool).
- Shell self stress = ρ_s v² at the mean wall radius; liquid pressure at the wall p = ρ_l ω² (r² − r₀²) ÷ 2.
- Liquid hoop stress = p (D + t) ÷ 2t (the thin-wall value of the thick cylinder tool); speed limit = n √(allowable ÷ total).
- Example: 1,118.2 g at the wall; 22.041 + 36.993 = 59.034 MPa; the limit is 2,603 rpm.
Limitations
- Thin plain cylinder; perforations in a basket raise the stress and the bowl ends, hubs and joints need their own checks.
- Liquid ring only; solids cake in a basket add pressure as a denser ring.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a centrifuge bowl before raising the speed
- Size the wall of a spinning drum
- Find the safe speed limit for a bowl
Who it is for
- Design engineers
- Process engineers
- Safety engineers
What you get
- Wall acceleration as g
- Hoop stress from the shell and from the liquid
- Total stress and speed limit
Interpreting the result
- Every stress in a spinning bowl rises with the square of the speed: 10% more speed means 21% more stress.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 187–190, 290–294. Topic reference; no source tables or recommended settings are reproduced.
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